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/* Dijkstra's dutch flag */
typedef enum { BLUE, WHITE, RED } color;
//@ predicate isColor(int i) { i == BLUE || i == WHITE || i == RED }
/*@ predicate isMonochrome(int t[], int i, int j, color c)
@ { \valid_range(t,i,j) && \forall int k; i <= k && k <= j => t[k] == c }
@*/
/*@ requires \valid_index(t,i) && \valid_index(t,j)
@ assigns t[i],t[j]
@ ensures t[i] == \old(t[j]) && t[j] == \old(t[i])
@*/
void swap(int t[], int i, int j);
/*@ requires n >= 0 &&
@ \valid_range(t,0,n-1) &&
@ (\forall int k; 0 <= k && k < n => isColor(t[k]))
@ assigns t[0 .. n-1]
@ ensures
@ (\exists int b, int r;
@ isMonochrome(t,0,b-1,BLUE) &&
@ isMonochrome(t,b,r-1,WHITE) &&
@ isMonochrome(t,r,n-1,RED))
@*/
void flag(int t[], int n) {
int b = 0;
int i = 0;
int r = n;
/*@ invariant
@ (\forall int k; 0 <= k && k < n => isColor(t[k])) &&
@ 0 <= b && b <= i && i <= r && r <= n &&
@ isMonochrome(t,0,b-1,BLUE) &&
@ isMonochrome(t,b,i-1,WHITE) &&
@ isMonochrome(t,r,n-1,RED)
@ variant r - i
@*/
while (i < r) {
switch (t[i]) {
case BLUE:
swap(t, b++, i++);
break;
case WHITE:
i++;
break;
case RED:
swap(t, --r, i);
break;
}
}
}
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